1. Polynomial and Rational Expressions

• Operations with Polynomials

• Addition, subtraction, multiplication, and division of polynomials

• Polynomial long division and synthetic division

• Factoring Polynomials

• Factoring by grouping, factoring trinomials

• Difference of squares, sum and difference of cubes

• Factoring completely

• Rational Expressions

• Simplifying rational expressions

• Operations with rational expressions (addition, subtraction, multiplication, division)

• Solving rational equations

2. Quadratic Functions and Equations

• Solving Quadratic Equations

• Factoring, using the quadratic formula, completing the square

• Solving quadratic equations in real-world contexts

• Quadratic Functions

• Standard form of a quadratic function: y=ax2+bx+cy = ax^2 + bx + c

• Graphing quadratic functions and identifying key features (vertex, axis of symmetry, direction of opening)

• Solving quadratic inequalities

3. Exponential and Logarithmic Functions

• Exponential Functions

• Definition and properties of exponential functions

• Graphing exponential growth and decay functions

• Applications of exponential functions (real-world applications such as population growth, radioactive decay)

• Logarithmic Functions

• Definition of logarithms, converting between exponential and logarithmic forms

• Properties of logarithms (product, quotient, power rules)

• Solving exponential and logarithmic equations

• Applications of logarithmic functions (e.g., pH, Richter scale, half-life problems)

4. Rational Functions

• Definition and Operations

• Identifying domain and range of rational functions

• Simplifying rational expressions and functions

• Graphing Rational Functions

• Vertical and horizontal asymptotes

• Identifying holes, x-intercepts, and y-intercepts of rational functions

• End behavior of rational functions

5. Radical Expressions and Equations

• Simplifying Radical Expressions

• Simplifying square roots and higher-order roots

• Operations with radicals (addition, subtraction, multiplication, division)

• Solving Radical Equations

• Solving equations involving square roots or higher-order roots

• Applications of Radicals

• Solving real-life problems involving square roots or cube roots

6. Sequences and Series

• Arithmetic Sequences

• Identifying and finding terms in arithmetic sequences

• Using the formula for the nth term of an arithmetic sequence

• Finding the sum of an arithmetic series

• Geometric Sequences

• Identifying and finding terms in geometric sequences

• Using the formula for the nth term of a geometric sequence

• Finding the sum of a finite or infinite geometric series

• Applications of Sequences and Series

• Real-world applications, such as finance, population models, etc.

7. Functions and Their Graphs

• Functions and Their Characteristics

• Domain and range of functions

• Transformations of functions (translations, reflections, stretches, and compressions)

• Operations on functions (addition, subtraction, multiplication, division, composition)

• Inverse functions

• Types of Functions

• Linear functions, quadratic functions, cubic functions

• Rational functions, exponential functions, logarithmic functions

• Piecewise functions

8. Systems of Equations and Inequalities

• Systems of Linear Equations

• Solving systems of equations using substitution, elimination, and graphing methods

• Systems of Nonlinear Equations

• Solving systems of equations that include quadratic, exponential, or other nonlinear functions

• Systems of Inequalities

• Graphing systems of inequalities

• Solving systems of linear inequalities and real-world applications

9. Statistics and Probability

• Descriptive Statistics

• Mean, median, mode, range, variance, and standard deviation

• Interpreting and analyzing data sets

• Probability

• Basic probability concepts (simple and compound events, independent vs dependent events)

• Probability distributions (binomial probability)

• Counting Principles

• Permutations and combinations

• Correlation and Regression

• Scatter plots and interpreting correlation coefficients

• Linear regression and best-fit lines

10. Conic Sections

• Circles

• Equation of a circle in standard form

• Graphing and identifying key features (center, radius)

• Parabolas

• Equation of a parabola in standard form y=a(x−h)2+ky = a(x-h)^2 + k

• Graphing parabolas and identifying key features (vertex, axis of symmetry)

• Ellipses and Hyperbolas

• Equations of ellipses and hyperbolas

• Graphing and identifying key features (center, axes, foci)

Test Format Overview

The Algebra 2 Regents Exam typically consists of:

• Multiple Choice Questions: Test your knowledge and understanding of algebraic concepts.

• Short-Answer Questions: Require you to solve problems and show your work.

• Extended Response/Essay Questions: Ask you to explain your reasoning and provide detailed solutions to more complex problems.

Key Skills for the Exam

• Understanding Functions: Be comfortable with the different types of functions and how to graph and manipulate them.

• Problem-Solving: Solve word problems by translating them into mathematical expressions or equations.

• Algebraic Manipulation: Simplify expressions, solve equations, and factor polynomials.

• Graphing and Interpretation: Graph functions and interpret the meaning of key features of the graphs.

Preparation Tips

• Practice Past Exams: Review previous Regents exams to become familiar with the types of questions.

• Use a Graphing Calculator: Know how to use your graphing calculator, especially for graphing functions and solving complex problems.

• Master Key Concepts: Ensure you understand core topics like solving equations, graphing, and working with functions.

• Work on Word Problems: Practice solving real-life problems that involve algebraic concepts.

This syllabus provides an overview of the topics covered on the Algebra 2 Regents Exam. To succeed, it’s important to review each of these areas thoroughly and practice applying these concepts to a variety of problems.

 

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